On Sat, Jul 2, 2011 at 4:57 PM, Bruno Marchal <[email protected]> wrote:
> > On 01 Jul 2011, at 13:23, selva kumar wrote: > > Is consciousness causally effective ? >> >> I found this question in previous threads,but I didn't find a answer. >> > > Was it in the FOR list (on the book Fabric of reality by David Deutsch) ? I > thought I did answer this question, which is a very imprtant and fundamental > question. > > It is also a tricky question, which is very similar or related to the > question of free-will, and it can lead to vocabulary issue. I often defend > the idea that consciousness is effective. Indeed the role I usually defend > for consciousness is a relative self-speeding up ability. Yet the question > is tricky, especially due to the presence of the "causally", which is harder > to grasp or define than "consciousness" itself. > > Let me try to explain. For this I need some definition, and I hope for some > understanding of the UDA and a bit of AUDA. Ask precision if needed. > > The main ingredient for the explanation are three theorems due to Gödel: > > - the Gödel completeness theorem (available for machine talking first order > logic or a sufficiently effective higher order logic). The theorem says that > a theory or machine is consistent (syntactical notion, = ~Bf) iff the theory > has a model (a mathematical structure in which it makes sense to say that a > proposition is true). I will rephrase this by saying that a machine is > consistent if and only if the machine's beliefs make sense in some reality. > > - the Gödel second incompleteness theorem ~Bf -> ~B(~Bf): if the machine is > consistent, then this is not provable by the machine. So if the beliefs are > real in some reality, the machine cannot prove the existence of that > reality. This is used in some strict way, because we don't assume the > machine can prove its completeness (despite this has shown to be the case by > Orey). This entails that eventually, the machine can add as new axiom its > own consistency, but this leads to a new machine, for which a novel notion > of consistency appears, and the 'new' machine can still not prove the > existence of a reality "satisfying its beliefs. yet that machine can easily > prove the consistency of the machine she was. This can be reitered as many > times as their are (constructive) ordinals, and this is what I describe as a > climbing from G to G*. The modal logic of self-reference remains unchanged, > but the arithmetical interpretation of it expands. An infinity of previously > undecidable propositions become decidable, and ... another phenomenon > occurs: > > - Gödel length of proof theorem. Once a machine adds an undecidable > proposition, like its own consistency, as a new axiom/belief, not only an > infinity of (arithmetical) propositions become decidable, but an infinity of > already provable propositions get shorter proofs. Indeed, and amazingly > enough, for any number x, we can find a proposition which proofs will be x > times shorter than its shorter proof in the beliefs system without the > undecidable proposition. A similar, but not entirely equivalent theorem is > true for universal computation ability, showing in particular that there is > no bound to the rapidity of computers, and this just by change of the > software (alas, with finite numbers of exceptions in the *effective* > self-speeding up: but evolution of species needs not to be effective or > programmable in advance). > > Extrapolating this and working this on human-machine,consider this.. If we firmly believe that all our proofs and instincts on mathematical truths are correct,will we get shorter proofs ? Now, this turns into a proof for existence of power of belief..(?). Also,speaking in a strict way,it means If you believe you are intelligent,then you become more intelligent (which is in immediate contracdiction with godel's second incompleteness theorem and your smallest theory on intelligence ) > Now I suggest to (re)define consciousness as a machine (instinctive, > preprogrammed) ability to bet on a reality. This is equivalent (stricto > sensu: the machine does not need to know this) to an ability of betting its > own consistency (excluding that very new axiom to avoid inconsistency). As a > universal system, this will speed-up the machine relatively to the probable > local universal system(s) and will in that way augment its freedom degree. > If two machines play ping-pong, the machine which is quicker has a greater > range of possible moves/strategy than its opponent. > > So the answer to the question "is consciousness effective" would be yes, if > you accept such definition. > > Is that consciousness *causally* effective? That is the tricky part related > to free will. If you accept the definition of free will that I often > suggested, then the answer is yes. Causality will have its normal "physical > definition", except that with comp such physicalness is given by an > arithmetical quantization (based on the material hypostase defined by Bp & > Dp): p physically causes q, iff something like BD(BDp -> BDq). I recall Dp = > ~B ~p. But of course, in God eyes, there is only true (and false) number > relations. The löbian phenomenon then shows that the consciousness > self-speeding up is coupled with the building of the reality that the > machine bet on. At that level, it is like if consciousness is the main > force, perhaps the only original one, in the physical universe! This needs > still more work to make precise enough. There is a complex tradeoff in > between the "causally" and the "effective" at play, I think. > > I hope this was not too technical. The work of Gödel plays a fundamental > role. This explanation is detailed in "Conscience et Mécanisme", and related > more precisely to the inference inductive frame. > > To sum up: machine consciousness, in the theory, confers self-speeding up > abilities to the machine with respect to the most probable > continuation/universal-**machine. It is obviously something useful for > self-moving creature: to make them able to anticipate and avoid obstacles, > which would explain why the self-moving creatures have developed > self-reflexive brains, and become Löbian (self-conscious). Note that here > the role is attributed to self-consciousness, and not really to > consciousness. But you need consciousness to have self-consciousness. > Consciousness per se has no role, like in pure contemplation, but once > reflected in the Löbian way, it might be the stronger causally effective > force operating in the 'arithmetical truth', the very origin of the (self) > acceleration/force. > Why do you always limit the definition of consciousness(atleast machine consciousness) to its ability to learn alone ? why shouldn't free-will and sensory experiences(qualia,if you believe in it)be part (rather than being a consequence or precondition) of consciousness itself ? In the absence of consciousness,there is indeed absence of free-will and experiencing qualia. In that case,we can't prove that a universal machine is conscious. > > Note that the Gödel speed-up theorem is not hard to prove. There is a > simple proof of it in the excellent book by Torkel Franzen "Gödel's theorem > An Incomplete Guide To Its Use and Abuse" which I recommend the reading > (despite it is more on the abuses than the uses). The original paper is in > the book by Davis: the undecidable (republished in Dover), and which I > consider as a bible for "machine's theology". > > Bruno > > http://iridia.ulb.ac.be/~**marchal/ <http://iridia.ulb.ac.be/%7Emarchal/> > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to > everything-list@googlegroups.**com<[email protected]> > . > To unsubscribe from this group, send email to everything-list+unsubscribe@ > **googlegroups.com <everything-list%[email protected]>. > For more options, visit this group at http://groups.google.com/** > group/everything-list?hl=en<http://groups.google.com/group/everything-list?hl=en> > . > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. 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